Similitude Analysis of Experiment and Modelling of Immiscible Displacement Effects with Scaling and Dimensional Approach

This paper presents the use of scaling and dimensional analysis to assess the viability of conventional modelling of immiscible displacement occurring when water is injected into the oil-saturated, porous rock—a conventional secondary oil-recovery method. A brief description of the laboratory tests of oil displacement with water performed on long core sets taken from wells operating on a Polish oil reservoir was presented. A dimensionless product generator based on dimensional analysis and Buckingham Π theorem was used to generate all possible combinatorial sets of dimensionless products for physical variables describing the phenomenon. The mathematical model of the phenomenon was transformed to its dimensionless form, using a selected set of the products. The results of the laboratory tests were analyzed as functions of the products. Statistically verified quantities describing both dependent and independent experiment variables were subject to a regression analysis to study dependencies of the experimental results upon selected dimensionless products. The degrees of the dependencies were determined and compared with the model coefficients. The conclusions are drawn for the purposes of model application to correctly describe the laboratory and, consequently, field scale processes of immiscible oil displacement by water.